Any convert may pursue and discern a vocation to the priesthood.
But the church generally asks a convert to wait a year, in case they are confusing the call to priesthood with a call to holiness where they are.

CatholicGirl15:

Someone told me that if an infant is baptized Catholic, but is raised Protestant, and then converts back to Catholicism as an adult, he can’t become a priest. Is this true?

Someone told me that if an infant is baptized Catholic, but is raised Protestant, and then converts back to Catholicism as an adult, he can’t become a priest. Is this true?

It probably comes from this canon law, however a heresy must be imputable to be a delict. This requires an act of will. The person may not have learned the Catholic faith, although baptized so this is significant. In any case, there would be an investigation upon application for seminary.

CIC
Can. 1041 The following are irregular for receiving orders:
…

2/ a person who has committed the delict of apostasy, heresy, or schism;
…

IRREGULARITIES AND SIMPLE IM PEDIMENTS IN THE NEW CODE OF CANON LAW BY THE JEV. JOHN J. RICKEY, S.T.B., J.C.L. (MARCH 18, 1920.)
44

“Heresy is a species of infidelity in men who, having professed the faith of Christ, corrupt its dogmas.” 7 “The heretical tenets may be adhered to from involuntary causes: inculpable ignorance of the true creed, erroneous judgment, imperfect apprehension and comprehension of dogmas. In none of these does the will play an appreciable part, wherefore one of the necessary conditions of sinfulness free choice is wanting and such heresy is merely objective, or material. On the other hand, the will may freely incline the intellect to adhere to tenets declared false by the divine teaching authority of the Church. The impelling motives are many: intellectual pride or exaggerated reliance on ones own in sight, the illusions of religious zeal, the allurements of political or ecclesiastical power, the ties of material interests and personal status ; and perhaps others more dishonorable. Heresy thus willed is imputable to the subject and carries with it various degrees of guilt; it is called formal because to the material error it adds the informative element of freely willed. Pertinacity, that is, obstinate adhesion to a particular tenet, is required to make heresy formal.” 8 The Code does not specify any particular species, hence one who is heretical in any sense, must contract this irregularity.

Just watching EWTN and reading a few books on the priesthood, I have observed the following:

Guys who leave the Catholic Church and return, spend their lives as atheists and convert later in life, have been alcoholics and drug addicts, are over 40 when they hear the call, are married and later divorced, have handicaps such as deafness or speech impediments or have had nervous breakdowns, may all be admitted into seminary and ultimately ordained to the priesthood. In other words, it is case-by-case.

Apparently, the only thing that ends any talk of discernment immediately with no allowance for further discussion is when a man (in the Latin Rite) who is currently married believes he may be called.

Latin Canon Law (CIC)Can. 1040 Those affected by any impediment, whether perpetual, which is called an irregularity, or simple, are prevented from receiving orders. The only impediments incurred, however, are those contained in the following canons.

Can. 1041 The following are irregular for receiving orders:[INDENT]1/ a person who labors under some form of amentia or other psychic illness due to which, after experts have been consulted, he is judged unqualified to fulfill the ministry properly;
2/ a person who has committed the delict of apostasy, heresy, or schism;
3/ a person who has attempted marriage, even only civilly, while either impeded personally from entering marriage by a matrimonial bond, sacred orders, or a public perpetual vow of chastity, or with a woman bound by a valid marriage or restricted by the same type of vow;
4/ a person who has committed voluntary homicide or procured a completed abortion and all those who positively cooperated in either;
5/ a person who has mutilated himself or another gravely and maliciously or who has attempted suicide;
6/ a person who has placed an act of orders reserved to those in the order of episcopate or presbyterate while either lacking that order or prohibited from its exercise by some declared or imposed canonical penalty.
Can. 1042 The following are simply impeded from receiving orders:1/ a man who has a wife, unless he is legitimately destined to the permanent diaconate;
2/ a person who exercises an office or administration forbidden to clerics according to the norm of cann. ⇒ 285 and ⇒ 286 for which he must render an account, until he becomes free by having relinquished the office or administration and rendered the account;
3/ a neophyte unless he has been proven sufficiently in the judgment of the ordinary.
[/INDENT]